How do I create a bumpy reflective material?
Creating a bumpy reflective material is easy using procedural textures and bump nodes.  

Step 1: Make sure that you are using Cycles Render
   

Step 2: Add a Bump Node With Shift+A, and under Vector choose Bump.  

Step 3: Connect the Normal output of the Bump node with the Normal input of the Material you are using (In most cases this will be a Diffuse material.)  

Step 4: Add a Voronoi Texture node with Shift+A, and under Texture choose Voronoi Texture.  

Step 5: Connect the Fac output of the Voronoi Texture node with the Height input of the Bump node.
You'll notice that this already begins to warp the lighting effects on your model the way that you would want them to. 

Step 5: Now you just have to adjust the Scale value of the Voronoi Texture node to your liking.
Also, adjust the Strength value on the Bump node, so that the effect on the lighting isn't as harsh.

Your end node setup should look something like this:
  

Note: This same process applies for any other Texture node, I just used Voronoi for example because it looks close to the effect OP is trying to achieve.